In how many ways can 6 different novels, 6 different mathematics books, and 2 biology book(s) be arrangedon a bookshelf if(a) The books can be arranged in any order? 14!(b) The mathematics books must be together and the novels must be together?(c) The mathematics books must be together, but the other books can be arranged in any order?

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Answered: ways cal on a bookshelf if 6 different…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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I have a permutations & combinations geometry question.
We have 3 Physics books, 4 Math books, and 5 Chemistrybooks. The 12 books are distinct. We want to arrange them all on abookshelf. Observe that without any restrictions there are 12! ways to arrangethem on a bookshelf. Explain each answer. In how many ways can we do this(a) if the arrangement must start with a Physics book and must end with aChemistry book?(b) if the arrangement cannot end with a chemistry book?(c) if the arrangement must begin with all the Physics books?(d) if the two specific books X and Y (of the 12 books) cannot be next toeach other?(e) if all the books belonging to a subject must stay together (i.e. stay nextto each other)? (hint: The subjects themselves have to be in someorder.)
(a) In how many ways can 4 boys and 3 girls sit in a row. (b) In how many ways can they sit in a row if the boys and girls dare each to sit together
A class consists of 15 boys and 12 girls. They want to elect officers so that the president and secretary are girls, and the vice president and treasurer are boys. (a) How many possibilities are there? possibilities (b) How many are there if 3 of the boys refuse to participate? possibilities Additional Materials
A class consists of 15 boys and 10 girls. They want to elect officers so that the president and secretary are girls, and the vice president and treasurer are boys. (a) How many possibilities are there? possibilities(b) How many are there if 3 of the boys refuse to participate? possibilities
Please help with these two parts
How many different 6-character license plates are possible if the first 4 places are to be occupied by numbers and the final 2 by letters? Repetition is possible and numbers may have leading zeroes. (a) 26! 10! * 4 * 2 (b) 264*10² (c) (26) (¹2) (d) 26² * 104 (e) None of the above
24, 30, 36, 42, ... Add an answer item! Answer Bank an -15n+23 8,-7,-22,-37,... -33, -21,-9, 3, ... Add an answer item! a=24+6(n-1) Add an answer item! -33 +12(n-1)

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